A holding cost bound for the economic lot-sizing problem with time-invariant cost parameters

In this paper we derive a new structural property for an optimal solution of the economic lot-sizing problem with time-invariant cost parameters. We show that the total holding cost in an order interval of an optimal solution is bounded from above by a quantity proportional to the setup cost and the logarithm of the number of periods in the interval. Since we can also show that this bound is tight, this is in contrast to the optimality property of the economic order quantity (EOQ) model, where setup cost and holding cost are perfectly balanced. Furthermore, we show that this property can be used for the design of a new heuristic and that the result may be useful in worst case analysis.